Companion plant
spacing calculator

Abstract

A popular
recommendation for
determining plant spacing in
mixtures does not account for component crop ratios
and results in lower total plant density than separate
plantings of component crops in pure stands. This method likely
compromises the yield advantage that should be expected from mixed
plantings. A new equation for calculating plant spacing in mixtures is
proposed. A spreadsheet and online spacing calculator, based on this
equation, are available for public use.

Background

Mixed
planting, or companion planting, can offer benefits over
monocultures:

Mixed crops often have higher
yields than monocultures because different species use different
resources, making more efficient use of land.1

Mixed plantings often
have fewer pest problems than monocultures because pests have a harder
time finding suitable hosts, or because diverse plantings provide
better habitat for natural enemies.2

Diversity helps
reduce risk. Promoting biodiversity is
a stated goal of the USDA's national organic standards.3

Some crops are commonly grown in mixtures. Hay, for example,
is
usually a mix of grass and legume species. Shade-grown coffee
plantations mix low-growing coffee bushes with trees. Backyard
gardeners often mix vegetables, herbs, and flowers in the same
bed.

Although mixed plantings are common, practical resources for
those
who grow mixed crops are few; production guides and extension materials
are often based on the assumption of monoculture.

Biointensive mini-farming

One practical guide for gardeners and small-scale producers
growing mixed plantings is the popular manual How to Grow More Vegetables,
by John Jeavons.4
It advocates a system
called "biointensive mini-farming," which consists of high-density
mixed plantings grown in offset rows in carefully-prepared soil.
Jeavons claims the system often yields twice as much
as conventional methods.

The book is distinguished by detailed tables and
diagrams
(unlike most books dealing with mixed plantings, which tell
you what to
mix, but not how).
Higher densities are achieved through tight plant spacing
and elimination of space between rows, so
that every plant is the same distance from its six nearest neighbors,
creating a beehive pattern of hexagons:

Hexagonal spacing diagram from How to Grow More Vegetables... (Jeavons
2006). The spacing between plants is equivalent within and between
rows, forming a hexagonal lattice of tightly-spaced plants.

For plant spacing in mixtures, Jeavons uses the mean
of his
recommended plant spacings for the component crops. For
example,
he suggests that corn
plants in monoculture be spaced 15" apart, and beet plants 4" apart, so
corn and beet planted as a mixture are spaced 9.5" ([15+4]/2)
apart:

Two-crop companion planting diagram from How to Grow More Vegetables...
(Jeavons 2006). The recommended spacings for corn (C) and beets (B) in
monoculture are 15" and 4" respectively. The book recommends a mean
spacing of 9.5" when the two crops are mixed.

The bed illustrated in this example covers approximately 60
sq. ft. with 33 corn plants and 80 beet plants. The plant
density is 5 corn plants and 12 beet plants per sq. yd., for a total
of 17 plants per sq. yd.:

Two-crop companion planting diagram with dimensions,
adapted from How
to Grow More Vegetables (Jeavons 2006). Corn plants are
represented by yellow circles; beets are red.

A pure stand of 33 corn plants spaced according
to Jeavons' recommendations requires 45
sq. ft. of bed space, and a pure stand of 80 beets requires 8 square
feet of bed space. Thus, the same number of plants grown in two pure
stands would require only 53 sq. ft. of bed space, leaving 7
sq.
ft. for another crop:

Pure stands of corn and beet plants, spaced
according to How to
Grow More Vegetables(Jeavons 2006).

The mixed planting arrangement in Jeavons' example has three
beet plants
for
every corn plant, but more than five times as much land dedicated to
corn
as to beets. What if the land were
evenly divided between the
two crops?

Dividing the 60 square-foot bed in half
would give room for 22 corn plants on one side and 309 beet plants on
the
other -- roughly 14 beets for every corn. To grow those same
331
plants in a mixture, with 9.5" between plants, would require 180 sq.
ft. -- three times as much land as the two pure stands
combined!

If crop mixtures make more efficient use of resources than
monocultures then mixed plantings should not require more land than
pure stands. The example above suggests two problems with the spacing
recommendations from How
to Grow More Vegetables:

The area available to a plant is proportional to
the square of plant spacing. (Plants spaced 13" apart in
a hexagonal lattice each have a square foot to grow, but plants
spaced 26" apart each get four square feet.)
Calculating the mean area per plant offers a better approximation of
the resources available to each plant in a mixture than the mean plant
spacing used by Jeavons.

The proportion of each crop in a mixture is crucial.
Calculating the mean plant spacing does not account for mixtures with
different component crop proportions.

To address these problems, I propose the following equation
to calculate plant spacing in a mixture:

where

sA
and sB
are the recommended pure stand spacings for crops A and B, respectively, and

p
is the proportion of plants in the mixture (a value between 0 and 1)
accounted for by crop A .

In the example above, corn accounts for one-quarter of the
plants in the mixture, so p=0.25.
The recommended spacings for corn and beets are 15" and 4",
respectively, so sA=15
and sB=4.
The calculated mixture spacing, according to the equation, is 8.25"
instead of 9.5".

In the case where corn accounts for only one-fifteenth of the
plants in the mixture, p=1/15=0.067,
so the plant spacing is only 5.5".

A spacing calculator for mixed plantings

Since using this equation is more complex than calculating
a mean, I have developed a new spacing calculator
for two-crop mixtures, available for download here
(Fig.4). A simpler online version, which can be used for mixtures of up
to four crops, is here.
Both calculate spacings for offset rows, based on the geometry
of hexagonal spacing arrangements and target crop ratios. The
spreadsheet allows the
user to select two crops and target ratios from drop-down
menus. Recommended plant spacings and densities are calculated in
metric and US measurement units.

This is a Microsoft Excel spreadsheet, created with Excel XP.
It may
not work with earlier versions of Excel or other spreadsheets. The
graphing feature requires the Analysis ToolPak Add-in for Excel (check
the Add-Ins feature under Excel's Tools menu if the graphs don't work),
but the graphs aren't necessary to calculate plant spacings.

Figure 4. A screenshot of the spacing calculator
spreadsheet being
used to calculate spacings for a mixed planting of corn and beets.

Using the spacing calculator spreadsheet

Select your preferred options using the drop-down menus for
the four yellow cells. The calculator does the rest.

Select your preferred source for monoculture spacing
recommendations. Three sources are built in:

a. In-bed spacing
recommendations from How
to Grow More Vegetables...4

The fourth option, labeled
"Custom," is
initially set to the mean of the other sources. Custom values can be
edited to reflect other recommendations or user preferences.

Where a range of
recommendations was provided by a particular source the median value
was used.

Select two crops using the drop-down menus for the yellow
cells. The first crop should be the one that requires more space.

Select a target ratio for the second crop. The "Even ratio"
column indicates the ratio that would devote the same land area to
each crop. For the corn/beet mixture in the example, 14.1 beets require
as much land as one corn plant. A target ratio of 15 beet plants for
every corn plant is the option that comes closest to an even corn/beet
mix. Select a target ratio that approximates your desired harvest.

A square
meter of
corn (white circles, left) and beets (black diamonds, right), planted
in monocultures using the hexagonal spacings recommended in How to Grow
More Vegetables... (Jeavons
2006).

A square
meter of corn and beets, grown in mixtures with corn:beet
ratios of 1:3 (left), 1:8 (center), and 1:15 (right) using plant
spacings
calculated by the spacing calculator.

Calculations conducted

1. Spacing

The distance between plants in a hexagonal lattice.
Spacing for each component crop, grown in monoculture, is provided
along with spacing for the mixture, in bold.

2. Row spacing

The distance between rows in a hexagonal lattice.

3. Area

The mean area dedicated to each plant.

4. Density

The number of plants in a given area. This may be
helpful for practitioners of Mel Bartholomew's "square foot
gardening" system.

5. Mixture spacing

The distance between plants of the same species in a
mixture.
For example, corn plants grown in a 1:15 corn:beet ratio will be spaced
four times further apart than beets (see Fig. 5B, right).

6. Mono. equiv. and
Mono. prop.

Measures of the relative amount of land needed to grow
the
plants used in a mixture in monocultures. For example, if the
plants used for a 1:3 mixture of corn and beets were instead divided
into two monocultures, the corn would fill 82% of the land, and the
beets would take the remaining 18%. The monoculture equivalent for
beets would be 0.18, and the monoculture proportions for corn and beets
would be 82 and 18%, respectively.